Related papers: On regularity properties of a surface growth model
Given a sequence of properly embedded minimal surfaces in a $3$-manifold with local bounds on area and genus, we prove subsequential convergence, smooth away from a discrete set, to a smooth embedded limit surface, possibly with…
Flows of granular media down a rough inclined plane demonstrate a number of nonlocal phenomena. We apply the recently proposed nonlocal granular fluidity model to this geometry and find that the model captures many of these effects.…
Understanding how amorphous solids yield under shear is central to predicting material failure, yet prescribing reliable local yielding criteria remains a fundamental challenge. Here, through a mesoscale analysis of localized yielding, we…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
In this paper, we study regularity estimates for a class of degenerate, fully nonlinear elliptic equations with arbitrary nonhomogeneous degeneracy laws. We establish that viscosity solutions are locally continuously differentiable under…
We establish higher regularity properties of solutions to fully nonlinear elliptic equations at interior critical points. The key novelty of our estimates lies in the fact that they yield smoothness properties that go beyond the inherent…
We prove a compactness theorem for metrics with Bounded Integral Curvature on a fixed closed surface $\Sigma$. As a corollary, we obtain a compactification of the space of Riemannian metrics with conical singularities, where an accumulation…
We study smoothness of densities for the solutions of SDEs whose coefficients are smooth and nondegenerate only on an open domain $D$. We prove that a smooth density exists on $D$ and give upper bounds for this density. Under some…
It is shown that, by imposing reparametrization invariance, one may derive a variety of stochastic equations describing the dynamics of surface growth and identify the physical processes responsible for the various terms. This approach…
Mean curvature flow of clusters of n-dimensional surfaces in R^{n+k} that meet in triples at equal angles along smooth edges and higher order junctions on lower dimensional faces is a natural extension of classical mean curvature flow. We…
In this note, we announce new regularity results for some locally integrable distributional solutions to Poisson's equation. This includes, for example, the standard solutions obtained by convolution with the fundamental solution. In…
We present some new regularity criteria for ``suitable weak solutions'' of the Navier-Stokes equations near the boundary in dimension three. We prove that suitable weak solutions are H\"older continuous up to the boundary provided that the…
We carry out a detailed quantitative analysis on the geometry of invariant manifolds for smooth dissipative systems in dimension two. We begin by quantifying the regularity of any orbit (finite or infinite) in the phase space with a set of…
In the study of local regularity of weak solutions to systems related to incompressible viscous fluids local energy estimates serve as important ingredients. However, this requires certain informations on the pressure. This fact has been…
A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…
We study the equations obtained from linearizing the compressible Navier-Stokes equations around a steady-state profile with a heavier fluid lying above a lighter fluid along a planar interface, i.e. a Rayleigh-Taylor instability. We…
We present a model for stable crack growth in a constrained geometry. The morphology of such cracks show scaling properties consistent with self affinity. Recent experiments show that there are two distinct self-affine regimes, one on small…
We establish the regularity results for solutions of nonlocal Venttsel' problems in polygonal and piecewise smooth two-dimensional domains.
We investigate the presence of localized solutions in models described by a single real scalar field with generalized dynamics. The study offers a method to solve very intricate nonlinear ordinary differential equations, and we illustrate…
We prove higher summability for the gradient of minimizers of strongly convex integral functionals of the Calculus of Variations with (p,q)-Growth conditions in low dimension. Our procedure is set in the framework of Fractional Sobolev…